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Hereditary Torsion Theories for Graphs

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Abstract

Using congruences, a Hoehnke radical can be defined for graphs in the same way as for universal algebras. This leads in a natural way to the connectednesses and disconnectednesses (= radical and semisimple classes) of graphs. It thus makes sense to talk about ideal-hereditary Hoehnke radicals for graphs (= hereditary torsion theories). All such radicals for the category of undirected graphs which allow loops are explicitly determined. Moreover, in contrast to what is the case for the well-known algebraic categories, it is shown here that such radicals for graphs need not be Kurosh–Amitsur radicals.

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Authors and Affiliations

  1. Nelson Mandela University, Port Elizabeth, South Africa

    S. Veldsman

  2. La Trobe University, Melbourne, Australia

    S. Veldsman

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  1. S. Veldsman
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Correspondence to S. Veldsman.

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Veldsman, S. Hereditary Torsion Theories for Graphs. Acta Math. Hungar. 163, 363–378 (2021). https://doi.org/10.1007/s10474-021-01134-w

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  • DOI: https://doi.org/10.1007/s10474-021-01134-w

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